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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to

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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink] New post   02 Jul 2023, 06:53
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If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)
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B
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Re: If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink] New post   02 Jul 2023, 06:57
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MasteringGMAT wrote:
If a = \(\sqrt{ 2}\) — 1 and b = 1, which of the following is equal to [\(a^2\) + b(b + 2a)] + [\(b^2\) + a(a + 2b)] ?


A. 2
B. 4
C. 2\(\sqrt{ 2}\)
D. 2+2\(\sqrt{ 2}\)
E. 4+2\(\sqrt{ 2}\)


[\(a^2\) + b(b + 2a)] + [\(b^2\) + a(a + 2b)]

\((a^2 + b^2 + 2ab) + (b^2 + a^2 + 2ab)\)

\(2(a+b)^2\)

Let's substitute the value of a and b

\(2(\sqrt{ 2} — 1+1)^2\)

\(2(\sqrt{ 2})^2\)

\(2* 2 = 4\)

Option B
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Re: If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink] New post   02 Jul 2023, 10:42
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MasteringGMAT wrote:
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)


MasteringGMAT is this question from GMATPrepNow or GMAC's GMAT Prep. Thank you!
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Re: If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink] New post   02 Jul 2023, 11:28
MasteringGMAT wrote:
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)


\(a^2 + b(b + 2a) = a^2 + b^2 + 2ab = (a + b)^2\)

\(b^2 + a(a + 2b) = b^2 + a^2 + 2ab = (a + b)^2\)

Now, \(a + b = \sqrt{2}— 1 + 1 = 2\)

Thus, \(a + b = 2\)

Hence, \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)] = (a + b)^2 + (a + b)^2 = 2 + 2 = 4\), Answer will be (B)
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Re: If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink] New post   02 Jul 2023, 22:50
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Bunuel wrote:
MasteringGMAT wrote:
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)


MasteringGMAT is this question from GMATPrepNow or GMAC's GMAT Prep. Thank you!



Thanks for checking Bunuel. I may have erroneously tagged it GMATPrepNow, but It should fall under GMAT Prep. I no longer have the option to change the tag. Will you be so kind to update the tag for this question?
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Bunuel
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink] New post   02 Jul 2023, 22:53
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MasteringGMAT wrote:
Bunuel wrote:
MasteringGMAT wrote:
If \(a = \sqrt{2}— 1\) and b = 1, which of the following is equal to \([a^2 + b(b + 2a)] + [b^2 + a(a + 2b)]\) ?


A. 2

B. 4

C. \(2\sqrt{ 2}\)

D. \(2+2\sqrt{ 2}\)

E. \(4+2\sqrt{ 2}\)


MasteringGMAT is this question from GMATPrepNow or GMAC's GMAT Prep. Thank you!



Thanks for checking Bunuel. I may have erroneously tagged it GMATPrepNow, but It should fall under GMAT Prep. I no longer have the option to change the tag. Will you be so kind to update the tag for this question?


No worries. Updated the tag. :)
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If a = 2^(1/2) - 1 and b = 1, which of the following is equal to [#permalink]
02 Jul 2023, 22:53
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